Question

2000 soldiers to start, and 60000 zombies to start, each soldier will kill 15 zombies a day, each soldier will recruit one new soldier the following day, each night zombies will infect 5 normal people, 20 million people in the city.

with 2,000 soldiers, is it enough if not, what is the minimum number of soldiers to stop the zombie spread. day 1 through day 10

million people in the city. st start with 2,000 soldiers. Is that enough soldiers? If not, then increase the number of soldi olve this problem by showing the MINIMUM number of soliders that would be needed to stop New Starting Zombies 60,000 Zombies Zombies Soldier New Total Soldiers killed Remaining Recruits Zombies zombies Day 1 2,000 30000 2 4000 60000120000 4000 600000 720000 3 8000 120000 600000 8000 3000000 3600000 4 16000 240000 3360000 16000 16800000 3600000 5 36000 540000 19620000 36000 300002000 150000 180000 20160000 16 19 20 Sheeti O Type here to search Background There's a zombie outbreak in a city of 20 million people and the army has been ordered to deal with it, and since you are the general, that means you have to decide what to do. One option is that you could send in all your troops, but then you would have none to spare if there's another outbreak somewhere else. Instead, you decide to send in a smaller force of just 2000 soldiers with orders to recruit members of the public to help them fight the zombies. This solution leaves you with plenty of soldiers in case there are any other outbreaks, but no one else thinks it will work. To prove them wrong, you set out to do the calculations. You know that each soldier can hunt down and kill 15 zombies a day. In the evening, each soldier can also recruit one new soldier from the people in the city who will join the army the following day and fight the zombies. However, each night the zombies will fight back and each one will infect five normal people who then become zombies. You know there's currently 60,000 zombies in the city. Have you made the right decision? Scenario 1. Calculate the number of zombies and soldiers at the start of each day from day 1 to day 10. If the number of zombies at the start of the day becomes 0, then the threat has been eliminated

Answer 1

Day Soldiers Zombies Killed Zombies Remain New Soldier Recruits New Zombies Total Zombies 60000 180000 720000 3600000 20160000 118080000 702720000 35040000004204800000 21004800000 25205760000 2000 2 4000 8000 416000 5 32000 6 64000 7 128000 8 256000 9 512000 10 1024000 2000 4000 8000 16000 32000 64000 128000 256000 150000 600000 30000 120000 600000 3360000 19680000 117120000 700800000 4200960000 25198080000 15360000151173120000 30000 60000 120000 240000 480000 960000 1920000 3840000 7680000 3000000 16800000 98400000 585600000 512000 125990400000 151188480000 1024000755865600000 907038720000

Day Soldiers Zombies Killed Zombies Remain New Soldier Recruits New Zombies Total Zombies 60000 135000 360000 1260000 5760000 30960000 178560000 8808000001056960000 2608000006312960000 3151680000037820160000 1280000 189004800000 226805760000 2500 5000 3 10000 4 20000 5 40000 6 80000 7 160000 8320000 9 640000 10 1280000 2500 5000 10000 20000 40000 80000 160000 320000 640000 37500 75000 150000 300000 600000 1200000 2400000 4800000 9600000 19200000 22500 60000 210000 960000 5160000 29760000 176160000 1052160000 6303360000 37800960000 112500 300000 1050000 4800000 25800000 148800000 2 2

Day Soldiers Zombies Killed Zombies Remain New Soldier Recruits New Zombies Total Zombies 60000 120060 240480 483120 979200 2036160 4538880 11877120 40550400 181877760 968417280 2666 5332 3 10664 4 21328 5 42656 6 85312 7 170624 8341248 9 682496 10 1364992 2666 5332 10664 21328 42656 85312 170624 341248 682496 1364992 1 39990 79980 159960 319920 639840 1279680 2559360 5118720 10237440 20474880 20010 40080 80520 163200 339360 756480 1979520 6758400 30312960 161402880 100050 200400 402600 816000 1696800 3782400 9897600 33792000 151564800 807014400

Day Soldiers Zombies Killed Zombies Remain New Soldier Recruits New Zombies Total Zombies 60000 119970 239760 478440 950400 1861920 3490560 5581440 2764800 44858880 326707200 -392048640 40005 80010 160020 320040 640080 1280160 2560320 5120640 10241280 20482560 19995 39960 79740 158400 310320 581760 930240 460800 7476480 65341440 2667 5334 10668 21336 42672 85344 170688 341376 682752 1365504 2667 5334 3 10668 4 21336 5 42672 6 85344 7 170688 8341376 9 682752 10 1365504 1 99975 199800 398700 792000 1551600 2908800 4651200 2304000 37382400
As we can see that as the soldiers become 2667 then the number of zombies after day 8 become negative i.e. the zombies are eliminated